NCERT Solutions for Class 10 Maths Chapter 1: Real Numbers

Introduction The NCERT Solutions for Class 10 Maths Chapter 1 “Real Numbers” help students understand important concepts like the Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, and properties of rational and irrational numbers. Exercise 1.1 focuses on basic problems related to these concepts.

Table of Contents

Topics Covered in Class 10 Maths Chapter 1: Real Numbers

Section Name	Topic Description
1	Introduction to Real Numbers
1.1	Euclid’s Division Lemma
1.2	The Fundamental Theorem of Arithmetic
1.3	Revisiting Irrational Numbers
1.4	Rational Numbers and Decimal Expansions
1.5	Summary

Real Numbers Class 10 Maths Objectives

Prove Euclid’s Division Lemma
State the Fundamental Theorem of Arithmetic
Find HCF and LCM using prime factorization
Establish whether a given number is irrational
Conclude whether the decimal expansion of a rational number is terminating or non-terminating repeating

Chapter 1 Class 10 Maths Real Numbers Summary

Euclid’s Division Lemma: Given positive integers a and b, there exist whole numbers q and r satisfying where .
Euclid’s Division Algorithm: Based on Euclid’s division lemma, the HCF of any two positive integers a and b (where ) is obtained as follows:
- Step 1: Apply the division lemma to find q and r where and .
- Step 2: If , the HCF is b. If , apply Euclid’s lemma to b and r.
- Step 3: Continue the process until the remainder is zero. The divisor at this stage will be . Also, .
The Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorized) as a product of prime numbers, and this factorization is unique, apart from the order of the prime factors.

Additional Information

We hope the NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1 help you. If you have any query regarding Maths NCERT Solutions Chapter 1 Real Numbers Exercise 1.1, drop a comment below and we will get back to you at the earliest.

Download NCERT Solutions for Class 10 Maths Chapter 1 PDF

Students can download the PDF for NCERT Solutions of Class 10 Maths Chapter 1 Real Numbers Exercise 1.1 for offline study. These solutions are extremely helpful while doing homework and revising before exams.

By using these solutions, students can achieve a better understanding and excel in their studies.

NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers is given below.

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